A "Big Bang" does not resolve Olbers' paradox

It would appear that having a "Big Bang" event would resolve Olbers' paradox: looking at stars further and further away means looking backwards in time, so after a certain distance no stars can be seen, and the paradox vanishes.

The statement that ""Big Bang" are still of bounded (but with no boundary conditions) universes" is not correct.
The inital singularity in time is independant
from whether the universe is open or closed, bounded or unbounded. The geometry of the universe is
a function of what is in the universe. You can have any
combination (open-closed, bounded-unbounded)
with or without a big bang.